Find the distance between these two points using the Pythagorean Theorem.

Question

(-3, 5) and (7, -1)
Which choice is correct?

(1 point)
Responses

62−−√+32=25−−√
square root of 6 squared end root plus 3 squared is equal to square root of 25

32−−√−52=20−−√
square root of 3 squared end root minus 5 squared is equal to square root of 20

(62+102)−−−−−−−−−√=136−−−√
square root of open paren 6 squared plus 10 squared close paren end root is equal to square root of 136

52+72=136−−−√

Answer 1

To find the distance between the points (-3, 5) and (7, -1) using the Pythagorean Theorem, we first find the change in the x-coordinates and the change in the y-coordinates:

1. Change in x: \( x_2 - x_1 = 7 - (-3) = 7 + 3 = 10 \)
2. Change in y: \( y_2 - y_1 = -1 - 5 = -6 \)

Now we can use the Pythagorean Theorem, which states:

\[ d = \sqrt{(change \ in \ x)^2 + (change \ in \ y)^2} \]

Substituting our values, we get:

\[ d = \sqrt{10^2 + (-6)^2} \]

Calculating the squares:

\[ d = \sqrt{100 + 36} \] \[ d = \sqrt{136} \]

Now, let's examine the provided choices for the correct representation of the distance calculation:

1. (62−−√+32=25−−√) - Incorrect
2. (32−−√−52=20−−√) - Incorrect
3. (62+102)−−−−−−−−−√=136−−−√ - Correct, because \( 10^2 + 6^2 = 136 \)
4. 52+72=136−−−√ - Incorrect

Based on these analyses, the correct choice is:

(62+102)−−−−−−−−−√=136−−−√.